常用数学公式

x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

$$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$

\sum_{i=1}^{n}\dfrac{ 1 } {n!} = e

$$\sum_{i=1}^{n}\dfrac{ 1 } {n!} = e$$

e^x = 1+ x+ \dfrac{x^2}{2!}+…….\dfrac{x^n}{n!}

$$e^x = 1+ x+ \dfrac{x^2}{2!}+.......\dfrac{x^n}{n!}$$

e^1 = e = 1+ \dfrac{1}{2!}+ x =1

$$e^1 = e = 1+ \dfrac{1}{2!}+$$

f(x) = f(x_0)+f’(x_0)(x-x_0)+\dfrac{f’‘(x_0)}{2!}(x-x_0)^2+………+\dfrac{f^n(x_0)}{n!}(x-x_0)^n

$$f(x) = f(x_0)+f'(x_0)(x-x_0)+\dfrac{f''(x_0)}{2!}(x-x_0)^2+.........+\dfrac{f^n(x_0)}{n!}(x-x_0)^n$$

x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}

$$x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

\lim_{x \to \infty}(1+\frac{1}{x})^{x} = e

$$\lim_{x \to \infty}(1+\frac{1}{x})^{x} = e$$

cos\theta =\frac{A \cdot B }{

A

\times B

}=\frac{\sum_{i=1}^{n}(A_{i}\times B_{i})}{\sqrt{\sum_{i=1}^{n}A_{i}^{2}} \times \sqrt{\sum_{i=1}^{n}B_{i}^{2}} }

$$cos\theta =\frac{A \cdot B }{|A||\times B|}=\frac{\sum_{i=1}^{n}(A_{i}\times B_{i})}{\sqrt{\sum_{i=1}^{n}A_{i}^{2}} \times \sqrt{\sum_{i=1}^{n}B_{i}^{2}} }$$ $$f(z) = tanh(z) = \dfrac{e^z-e^{-z}}{e^z+e^{-z}}$$ $$f^{'}(z)=1-f(z)^{2}$$ $$J(W,b;x,y)=\frac{1}{2}||h_{W,b}(x)-y||^{2}$$ $$J(W,b)=[\frac{1}{m}\sum_{i=1}^{m}J(W,b;x^{i},y^{i})]+\frac{\lambda}{2}\sum_{l=1}^{n_{l}-1}\sum_{i=1}^{s_{t}}\sum_{j=1}^{s_{t}+1}(W_{ji}^l)^2 = [\frac{1}{m}\sum_{i=1}^{m}\frac{1}{2}||h_{W,b}(x)-y||^{2}]+\frac{\lambda}{2}\sum_{l=1}^{n_{l}-1}\sum_{i=1}^{s_{t}}\sum_{j=1}^{s_{t}+1}(W_{ji}^l)^2$$